Numerical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach.

In this paper, we numerically study the water wave model with a nonlocal viscous term u t + u x + β u x x x + ν D 1 / 2 u ( t ) + γ u u x = α u x x , where D 1 / 2 u ( t ) = 1 π ∂ ∂ t ∫ 0 t u ( s ) t − s d s is the Riemann‐Liouville half‐order derivative in time. We propose and compare different numerical schemes based on the diffusive realizations of fractional operators. [ABSTRACT FROM AUTHOR]